So, AdS-Schwarzschild space time metric in the
Regge-Wheeler (RW) tortoise coordinate \(r\)  [1]} will be written as follows:
\(ds^{2}=e^{2A(r)}f^{\frac{3}{5}}(r)\left[dt^{2}-\frac{\left(d\vec{x}\right)^{2}}{f(r)}-dr^{2}\right]\) 
